Nuprl Lemma : req-vec_weakening
∀[n:ℕ]. ∀[x,y:ℝ^n]. req-vec(n;x;y) supposing x = y ∈ ℝ^n
Proof
Definitions occuring in Statement :
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
nat: ℕ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
req_wf,
squash_wf,
true_wf,
real_wf,
int_seg_wf,
iff_weakening_equal,
req_weakening,
req_witness,
equal_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. req-vec(n;x;y) supposing x = y
Date html generated:
2016_10_26-AM-10_14_41
Last ObjectModification:
2016_09_24-PM-09_33_50
Theory : reals
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