Nuprl Lemma : msep_functionality
∀[X:Type]. ∀d:metric(X). ∀x,y,x',y':X. (x ≡ x' ⇒ y ≡ y' ⇒ {x # y ⇐⇒ x' # y'})
Proof
Definitions occuring in Statement :
msep: x # y,
meq: x ≡ y,
metric: metric(X),
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
msep: x # y,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
uimplies: b supposing a,
rev_implies: P ⇐ Q
Latex:
\mforall{}[X:Type]. \mforall{}d:metric(X). \mforall{}x,y,x',y':X. (x \mequiv{} x' {}\mRightarrow{} y \mequiv{} y' {}\mRightarrow{} \{x \# y \mLeftarrow{}{}\mRightarrow{} x' \# y'\})
Date html generated:
2020_05_20-AM-11_38_54
Last ObjectModification:
2020_01_06-PM-00_15_08
Theory : reals
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