diff --git a/diffeomorphic_approx_3d_lp_le2_v2.txt b/diffeomorphic_approx_3d_lp_le2_v2.txt
index 2a65a7b..375d430 100644
--- a/diffeomorphic_approx_3d_lp_le2_v2.txt
+++ b/diffeomorphic_approx_3d_lp_le2_v2.txt
@@ -169,7 +169,7 @@ diffeomorphism g : Omega -> Omega' with
 
 Theorem A then follows: take the locally bi-Lipschitz H of Theorem B
 with a very small error, smooth it with Theorem C with a still smaller
-error, and use the triangle inequality. Every approximant
+error, and use the triangle ineuality. Every approximant
 keeps the target Lambda by construction, not by a limit argument.
 
 Qualitative topology in three dimensions gives replacements but no
@@ -244,7 +244,7 @@ rank two by compressing the kernel to a line or plane section.
 Both steps are local and summability over compact exhaustions of the
 open domains does the rest. For p = 1 the derivative control uses an
 elementary squared length-defect estimate followed by Holder's
-inequality, never strict convexity of the L^1 norm.
+ineuality, never strict convexity of the L^1 norm.
 
 Sketch of Theorem C (smoothing).
 
@@ -1158,7 +1158,7 @@ B_Q(5) the update
         |G(A(x)) - H(x)| <= |G(A(x)) - H(A(x))| + K_P |A(x) - x|.
 
 Divide by the local cube size l_Q. Interacting patches bring only the
-bounded ratios from Lemma 7.2 into this inequality. So for a fixed
+bounded ratios from Lemma 7.2 into this ineuality. So for a fixed
 number of stages the tolerances are assigned by backward recursion:
 
         Start with the desired final value bound;
@@ -1333,7 +1333,7 @@ the single global map L there. Lemma 7.5 and the chosen thresholds
 supply the input accuracy of Lemma 7.4. Supports B_Q(5) of one color
 are disjoint, so these insertions are simultaneous. Their local
 finiteness makes the union a domain homeomorphism. The value
-invariants follow from the update inequality. At the
+invariants follow from the update ineuality. At the
 end of this round the map agrees with L on every good cube and on a
 protected neighborhood of it.
 
@@ -2434,7 +2434,7 @@ counted hits: the local block-counting is exactly what Lemma 10.6
 controls.
 
 By Lemma 10.6, the expected weighted cost is at most C_dim times the
-source energy, with C_dim absolute. By Markov's inequality, for any
+source energy, with C_dim absolute. By Markov's ineuality, for any
 delta > 0, the probability that the weighted cost exceeds
 (Kappa(x)/delta) times the local source energy is at most delta.
 
@@ -2829,7 +2829,7 @@ image-area formula or 2D Lusin.
 
 On K_i the trace-test integrand is at most delta^p; off K_i it is at
 most C_M (1 + |Df|^p), whose excess integral is small. Markov's
-inequality therefore makes the failed volume small relative to the
+ineuality therefore makes the failed volume small relative to the
 fixed threshold tau^p. QED
 
 Kernel section parametrizations. Recall the notation y in Im D_1,
@@ -2893,7 +2893,7 @@ Section leftover. On each fixed section, first discard points where
 the tangential derivative differs substantially from the injective
 y-columns of D_1. On the retained set its two singular values lie
 between bounds depending only on M. The trace test (Lemma 11.3) and
-Chebyshev's inequality show that the discarded integral of
+Chebyshev's ineuality show that the discarded integral of
 1 + |D_y f|^p is at most C_M tau^p h^2. Select compact C^1 Lusin jet
 sets in the interiors of the original tiles, losing an arbitrary
 small additional integral. The jets extend to ambient charts b by
@@ -3082,7 +3082,7 @@ g : Omega -> Lambda with
 
 Compose. Take the H produced by Stage one with tolerances (eps/2, xi/2),
 then the g produced by Stage two applied to this H with tolerances
-(eps/2, xi/2). The triangle inequality gives
+(eps/2, xi/2). The triangle ineuality gives
 
         || g - f ||_{W^{1,p}}
           <= || g - H || + || H - f || < eps/2 + eps/2 = eps,