Nuprl Lemma : stable__reqmatrix
∀[a,b:ℕ]. ∀[X,Y:ℝ(a × b)]. Stable{X ≡ Y}
Proof
Definitions occuring in Statement :
reqmatrix: X ≡ Y,
rmatrix: ℝ(a × b),
nat: ℕ,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reqmatrix: X ≡ Y,
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
rmatrix: ℝ(a × b),
so_apply: x[s],
implies: P ⇒ Q,
stable: Stable{P},
uimplies: b supposing a
Lemmas referenced :
stable__all,
int_seg_wf,
req_wf,
stable_req,
req_witness,
rmatrix_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality_alt,
functionEquality,
productElimination,
applyEquality,
universeIsType,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
isect_memberEquality_alt,
dependent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
isectIsTypeImplies
Latex:
\mforall{}[a,b:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}(a \mtimes{} b)]. Stable\{X \mequiv{} Y\}
Date html generated:
2019_10_30-AM-08_13_13
Last ObjectModification:
2019_09_19-AM-10_49_45
Theory : reals
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