Nuprl Lemma : reqmatrix_weakening
∀[a,b:ℕ]. ∀[X,Y:ℝ(a × b)]. X ≡ Y supposing X = Y ∈ ℝ(a × b)
Proof
Definitions occuring in Statement :
reqmatrix: X ≡ Y,
rmatrix: ℝ(a × b),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
reqmatrix: X ≡ Y,
rmatrix: ℝ(a × b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
nat: ℕ
Lemmas referenced :
req_wf,
squash_wf,
true_wf,
real_wf,
subtype_rel_self,
iff_weakening_equal,
req_weakening,
int_seg_wf,
req_witness,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
applyEquality,
thin,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
inhabitedIsType,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
functionIsTypeImplies,
equalityIstype,
isect_memberEquality_alt,
isectIsTypeImplies,
functionIsType
Latex:
\mforall{}[a,b:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}(a \mtimes{} b)]. X \mequiv{} Y supposing X = Y
Date html generated:
2019_10_30-AM-08_13_39
Last ObjectModification:
2019_09_19-AM-10_53_35
Theory : reals
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