Nuprl Lemma : psub_weakening
∀a,b:formula(). a ⊆ b supposing a = b ∈ formula()
Proof
Definitions occuring in Statement :
psub: a ⊆ b,
formula: formula(),
uimplies: b supposing a,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
psub: a ⊆ b,
pvar: pvar(name),
formula_ind: formula_ind,
subtype_rel: A ⊆r B,
pnot: pnot(sub),
or: P ∨ Q,
pand: pand(left;right),
por: por(left;right),
pimp: pimp(left;right),
guard: {T}
Lemmas referenced :
formula-induction,
isect_wf,
equal_wf,
formula_wf,
psub_wf,
equal-wf-T-base,
atom_subtype_base,
pnot_wf,
or_wf,
pand_wf,
por_wf,
pimp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesis,
hypothesisEquality,
independent_functionElimination,
isect_memberFormation,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
axiomEquality,
rename,
inlFormation,
because_Cache
Latex:
\mforall{}a,b:formula(). a \msubseteq{} b supposing a = b
Date html generated:
2018_05_21-PM-08_52_49
Last ObjectModification:
2017_07_26-PM-06_16_05
Theory : general
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